Size alone doesn't set the surface area-to-volume ratio
- The idea
- Predict
- See it
- Why
- Check
The idea
“The smaller cell always has the higher surface area-to-volume ratio. Same volume means same surface.”
Shrink a cube and its ratio really does go up. That's true, so it's easy to stop there and skip the shape.
The short version
The mistake: The smaller cell always has the higher surface area-to-volume ratio. Same volume means same surface.
What's actually true: Size predicts the ratio only when shape stays the same. Flattening or folding adds surface with little or no added volume.
- Surface area-to-volume ratio is membrane area divided by volume. Everything a cell exchanges crosses its membrane, so a higher ratio serves each bit of cytoplasm faster.
- When shape stays the same, growing lowers the ratio. Volume grows with the cube of the width, but surface only with the square.
- Shape changes that. A flat, long and thin, or folded cell has more surface than a round one of the same volume.
On the exam: Before you compare sizes, check the shape. Flat, thin or folded cells can beat smaller ones.